- Thread starter
- #1

- Jun 22, 2012

- 2,918

On page 282 the Corollary to Theorem 5 states the following: (see attachment for Theorem 5 and the Corollary)

------------------------------------------------------------------------------------------------------------------------

**Corollary.**Let [TEX] E \supseteq F [/TEX] be fields and let [TEX] u \in E [/TEX] be algebraic over F .

If [TEX] v \in F(u) [/TEX], then v is also algebraic over F and [TEX] {deg}_F(v) [/TEX] divides [TEX] {deg}_F(u) [/TEX].

------------------------------------------------------------------------------------------------------------------------

The proof begins as follows:

"

**Proof.**Here [TEX] F(u) \supseteq F(v) \supseteq F [/TEX] ... ... etc etc

My problem is as follows:

How do you show formally and explicitly that [TEX] F(u) \supseteq F(v) \supseteq F [/TEX]

Would appreciate some help.

Peter